What is the integral from 0 to pi of (1-cos(2x)) ?

The integral from 0 to pi of (1-cos(2x)) is pi

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integral from 0 to pi of (1-cos(2x))

\int_{0}^{π} (1 - cos (2 x)) d x

π

Solution steps

\int_{0}^{π} 1 - cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{π} 1 d x - \int_{0}^{π} cos (2 x) d x

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (2 x) d x = 0

= π - 0

Simplify

= π

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What is the integral from 0 to pi of (1-cos(2x)) ?
The integral from 0 to pi of (1-cos(2x)) is pi